Sebastian,
I'm parsing the error messages of Mathematica 6 here. Maybe there are
further undocumented methods and options.
The method should be either Automatic or Arnoldi.
A call should be formed, for example, like this:
Eigenvalues[H, 1, Method -> {Arnoldi, MaxIterations -> 10000, Criteria
-> RealPart}]
the extra options are:
Shift (a complex number)
Tolerance (non-negative real number or Automatic)
BasisSize (integer >2 and <= matrix size)
MaxIterations (integer)
StartingVector (a vector of length equal to the matrix size)
Criteria: can be
Magnitude
RealPart
ImaginaryPart
BothEnds (for real symmetric eigenvalue problems only)
To know what these mean, I recommend the ARPACK documentation:
http://www.caam.rice.edu/software/ARPACK/
Briefly, the basis size option gives the number of vectors used in the
iteration; not even the authors of ARPACK seem to know an optimal
choice here. The criteria specify which n eigenvalues are to be
computed: those with largest magnitude, largest real part, or largest
imaginary part. "BothEnds" computes alternating eigenvalues with small
and large real parts. "Shift" is for shifting the spectrum around
(shift-invert method) to pick out eigenvalues from the center of the
spectrum, close to a previously known value.
hth
Roman.